# Adam starts with the number z=1+2i on the complex plane. First, he dilates z by factor of 2 about the origin. Then, he reflects it across the real axi

Adam starts with the number z=1+2i on the complex plane. First, he dilates z by factor of 2 about the origin. Then, he reflects it across the real axis. Finally, he rotates it ${90}^{\circ }$ counterclockwise about the origin. The resulting complex number can be written in form a+bi where a and b are real numers. What is the resukring complex number?
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wornoutwomanC
Adam starts with complex number Z=1+2i
After getting dilated by a factor of 2 , Z becomes 2+4i
Then the number is reflected across the real axis, so the number becomes 2-4i
Now, the resulting number is rotated ${90}^{\circ }$ anticlockwise .
we know if point (a, b) is rotated anticlockwise by the angle α, then we get point $\left(a\mathrm{cos}\alpha -b\mathrm{sin}\alpha ,b\mathrm{cos}\alpha +a\mathrm{sin}\alpha \right)$ so (2,-4) after gets rotated 90°anticlockwise becomes $\left(2{\mathrm{cos}90}^{\circ }+4{\mathrm{sin}90}^{\circ },-4{\mathrm{cos}90}^{\circ }+2{\mathrm{sin}90}^{\circ }\right)=\left(4,2\right).$
So, the resulting complex number is 4+2i